Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Factoring Polynomials
1:35 minutes
Problem 12a
Textbook Question
Textbook QuestionExpress the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars, for example, |x|. For any real number x, the absolute value is defined as |x| = x if x is greater than or equal to zero, and |x| = -x if x is less than zero.
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Distance Between Two Numbers
The distance between two numbers on the number line can be calculated using the absolute value of their difference. Specifically, the distance d between two numbers a and b is given by the formula d = |a - b|. This formula ensures that the distance is always a non-negative value, reflecting the concept of distance in a geometric sense.
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Evaluating Absolute Value
Evaluating absolute value involves substituting a specific number into the absolute value expression and simplifying it. For example, to evaluate |x| for x = -17, you would find that |-17| = 17. This process is essential for solving problems that require finding distances or magnitudes, as it translates the abstract concept of distance into a concrete numerical value.
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Related Practice
Textbook Question
In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.
x² - 4
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Factoring Polynomials practice set
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